I have recently encountered the following in a paper: Given $(\boldsymbol{z}-\boldsymbol{y(x)})^TU(\boldsymbol{z}-\boldsymbol{y(x)})$ where $U$ is a positive definite matrix independent of $x$ and $\boldsymbol{z}$ is also independent, the gradient with respect to $\boldsymbol{x}$ is:
$2\boldsymbol{\Delta}^TU[\boldsymbol{z}-\boldsymbol{y(x)}]$
where $\boldsymbol{\Delta}$ is the Jacobian of $\boldsymbol{y}$.
How does one show this?